Importance of broken geometric symmetry of single-atom Pt sites for efficient electrocatalysis

Platinum single-atom catalysts hold promise as a new frontier in heterogeneous electrocatalysis. However, the exact chemical nature of active Pt sites is highly elusive, arousing many hypotheses to compensate for the significant discrepancies between experiments and theories. Here, we identify the stabilization of low-coordinated PtII species on carbon-based Pt single-atom catalysts, which have rarely been found as reaction intermediates of homogeneous PtII catalysts but have often been proposed as catalytic sites for Pt single-atom catalysts from theory. Advanced online spectroscopic studies reveal multiple identities of PtII moieties on the single-atom catalysts beyond ideally four-coordinated PtII–N4. Notably, decreasing Pt content to 0.15 wt.% enables the differentiation of low-coordinated PtII species from the four-coordinated ones, demonstrating their critical role in the chlorine evolution reaction. This study may afford general guidelines for achieving a high electrocatalytic performance of carbon-based single-atom catalysts based on other d8 metal ions.


Non-Faradaic O 2 formation during online DEMS measurements
For product analysis, online differential electrochemical mass spectrometry (DEMS) measurement was conducted for Pt1(X)/CNTs (X = 0.15, 1, and 3), which enables a potentialresolved quantification of gaseous or volatile products in situ. The ionic currents for m/z = 32 and 35 were recorded to identify the main products of oxygen evolution reaction (OER) and chlorine evolution reaction (CER), i.e., O2 and Cl2, during two slow cyclic voltammograms (CVs). In addition, we further take into account the possible Cl2 hydrolysis before introducing into the mass spectrometer (including an electrolyte, a porous polytetrafluoroethylene (PTFE) membrane, and a capillary connecting the electrochemical flow cell and mass spectrometer) according to the following equation: Cl2 + H2O → HCl + HOCl 1,2 . Thus, the ionic currents for m/z = 36 and 51 were additionally monitored for HCl and HOCl, respectively.
For all Pt1(X)/CNTs, the online DEMS results reveal a predominant ionic current for m/z = 35 (Cl + ) in 0.1 M HClO4 + 1 M NaCl electrolyte, which corresponds to the fragmentation of Cl2 and its hydrolyzed derivatives, i.e., HCl and HOCl ( Fig. 1 and Supplementary Fig. 14).
Concurrently, distinct ionic currents for m/z = 36 and 51 (HCl + and OCl + , respectively) are detected, indicating the formation of HCl and HOCl during CER. An insignificant ionic current for m/z = 32 (O2 + ) is identified, corresponding to the molecular ion of O2, although the Pt1(X)/CNTs exhibited almost 100% selectivity toward CER based on the rotating ring disk electrode (RRDE) measurements ( Supplementary Fig. 6).
This discrepancy possibly originates from the further HOCl decomposition in the vacuum system, forming O2 as a product by the following equation: 2HOCl → 2HCl + O2 1,2 . To confirm the aforementioned scenario for O2 formation, we further performed an identical experiment in the absence of NaCl in the electrolyte. Contrasting with the results obtained in the presence of NaCl, the DEMS results reveal no detectable signals for O2 and Cl2 formation during CVs (Fig.   1c). Given that 1) O2 formation does not occur without Cl2 evolution, and 2) the potential range for O2 formation closely matches those of Cl2 and HOCl formations, we can reasonably conclude that the O2 signal during CER, as shown in Fig. 1b and Supplementary Fig. 14, is not a result of Faradaic reaction, i.e., OER, but an artifact resulting from the Cl2 hydrolysis and subsequent HOCl decomposition in the vacuum system of our DEMS setup.

Computational details
Electronic structure calculations for periodically replicated appropriate models were performed using the Vienna ab initio simulation package (VASP 5.4.1) based on the framework of density functional theory (DFT) 3 . The exchange-correlation potential was treated as in the generalized gradient approximation (GGA) with form proposed by Perdew-Burke-Ernzerhof (PBE) 4 . The valence electron density was expanded on a plane wave basis set with an optimal kinetic energy cutoff of 415 eV since test calculations for the *, *Cl, *O, and *OCl adsorbates with a kinetic energy cutoff of 600 eV indicate that the total energies are affected by at most 0.01 eV. The projected augmented wave (PAW) method 5 , as implemented in VASP by Kresse and Joubert 6 , was used to take into account the effect of core electrons on the valence electron density. To model the Pt-Nx sites, graphene-like patch cluster models were used with two carbon rings surrounding the Pt-Nx active sites, capped with H-bonds. This avoids using an exceedingly large supercell in a periodic approach necessary to avoid the long-range distortion on graphene induced by the Pt-Nx sites while large enough to lead to converged results. To carry out the necessary numerical integrations in the reciprocal space, the Brillouin zone was sampled using a 4×4×1 k-point Γ-centered Monkhorst-Pack grid. Using the Γ-point only results in a difference of the total energy of at most 0.01 eV. A convergence criterion of 10 −5 eV was used for the total energy, while the relaxation of atomic positions was stopped when forces acting on all relaxed atoms were smaller than 0.01 eV Å −1 . The calculation of vibrational frequencies for the optimized geometries was carried out by taking the elements of the Hessian matrix as finite differences of analytical gradients with intervals of 0.03 Å. A vacuum width of 25 Å was added to the x-and y-direction (along the plane direction defined by the employed models), whereas a vacuum width of 20 Å was added in the z-direction in all cases to avert artificial interactions between the periodically repeated models. An effective description of the dispersion interactions was included using the Grimme's DFT-D3 method 7 . The adsorption energy was calculated as follows: where Esub is the energy of relaxed Pt-N4 or Pt-N3(V), Ei is the energy of the reference molecule, and Ei/sub is the energy of the intermediate adsorbed on the active Pt sites of Pt-N4 or Pt-N3(V).
Based on this definition, it follows the more negative the Eads value, the more stable the adsorption structure.
The CER/OER performance was evaluated by calculating the free-energy changes (∆G) for each elementary reaction step according to the following equation: where ∆E corresponds to Eads (cf. Equation (1)), ∆EZPE is the change in zero-point energy for the step of interest, T is the temperature in Kelvin, and ΔS is the change in entropy. ∆EZPE was obtained directly from the calculated vibrational frequencies in the harmonic approximation, whereas the T∆S term requires evaluating the vibrational partition functions, which are also related to the vibrational frequencies 8 .

Surface Pourbaix diagrams
In this study, the free energies of the intermediate structures (*Cl, *OCl, *O, *OH, and *OOH) were considered for Pt-N4 and Pt-N3(V). To include the applied electrode potential, U, in the analysis of free-energy changes, the computational hydrogen electrode approach (CHE) was used 9 . This was achieved by considering the stoichiometric coefficients of the transferred electrons (e − ) and protons (H + ), denoted as ν(e − ) and ν(H + ), respectively, when compiling reaction equations for each adsorption process 10 . We derive the following formula: The value of 0.059 eV was derived from the term kBT · ln10 evaluated at room temperature, where kB is Boltzmann's constant and U is the applied electrode potential on the standard hydrogen electrode (SHE) scale 11 .
The most thermodynamically favorable structure was determined by the minimization of the ΔG values for each adsorbate among the set of considered surface structures. The resulting surface phase (Pourbaix) diagram is shown as a function of overpotential η, defined by η = U − 1.36 V. For the analysis, the pH was fixed at zero, because we aimed to comprehend trends for the anodic CER in an acidic medium 12 . Hence, we are not discussing pH effects for which the application of grand canonical schemes is called for 13 .

Mechanistic studies: Assessment of electrocatalytic activity
Free-energy diagrams for the CER over Pt-N4 and Pt-N3(V) were constructed to evaluate the CER activity of these active sites. Based on the knowledge gained in previous studies [14][15][16] , the CER was assumed to proceed via the Volmer-Heyrovsky mechanism 17,18 . Two different Volmer-Heyrovsky pathways with dissimilar intermediates (i.e., *Cl or *OCl) were considered in our theoretical study 19 .
(I) Pathway mediated by the *Cl intermediate: (II) Pathway mediated by the *OCl intermediate: .
The free energy of chloride in solution, G (Cl − aq), is related to that of the Cl2 gas molecule as follows: Consequently, the ΔGj values for each elementary step are given by: .
Therefore, the ΔG values for each elementary step are: , , , To quantify the electrocatalytic activity for the CER and OER, the recently introduced descriptor Gmax (U), which is an activity measure that goes beyond the conventional approach in terms of the thermodynamic overpotential only, was used 21,22 . This descriptor relies on a free-energy span model by extracting the largest free-energy difference between intermediate states at a given target electrode potential: .
For further information on how to define the free-energy spans, Gspan #k (U), for a two-electron (CER) or four-electron process (OER), we refer the reader to recent publications by the authors 23,24 .

Selectivity assessment
The descriptor Gmax (U) was extracted for both OER and CER at well-defined electrode potentials, U >1.36 VSHE. The free-energy difference, Gsel (U), defined as is a measure of the CER selectivity 25 . This quantity was used to determine the CER selectivity in percentage using the following relation 19,25 : CER selectivity (U) = .

Stability assessment
Considering that PtO2 is the preferred state of Pt under CER conditions 26 , the tendency of the active Pt II sites toward oxidative demetallation to PtO2 was analyzed for Pt-N4 and Pt-N3(V). We note that the Udiss value cannot be used to explain why Pt-N3(V) is first formed when the Pt loading is low. We believe that the formation of Pt-N3(V) for low Pt loadings is governed by a kinetic reaction control, whereas with higher Pt loadings, the formation of Pt-N4 prevails since this configuration is thermodynamically preferred (thermodynamic reaction control), as evident from its larger Udiss value.

Supplementary Figures and Tables
Supplementary Fig. 1: a-  Pt−N indicates a single scattering path of the first-shell. Pt … C indicates a single scattering path of the second-shell (Shell column). The CN is the coordination number obtained from the amplitude reduction factor (S0 2 ) of 0.84. R indicates bond distance. σ 2 indicates the Debye-Waller factor. ΔE0 indicates the energy shift. R-factor was obtained from the best fit for the respective catalysts. (*Defined parameters to reduce correlations between variables)